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        <title>The &lt;10 Target Molecule Problem</title>
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        <h1 align="center">wThe &lt;10 Target Molecule Problem</h1>
		<p align="left">Note that the data presented here was taken from:
		Rutledge RG, Stewart D (2010) Assessing the performance capabilities of 
		LRE-based assays for absolute quantitative real-time PCR. PLoS ONE 5: 
		e9731. </p>
		<p align="left">Note also that the third LRE Overview video provided on the LRE qPCR website (<font color="#FF0000">sites.google.com/site/lreqpcr</font>) 
		presents a more detailed discussion of these datasets, along with how Poisson distribution 
		can be used to conduct absolute quantification. </p>
		<p><b>Scattering of replicate profiles<br>
		</b>In contrast to most samples which produce closely clustered replicate profiles, samples containing &lt;10 target molecules can produce 
		highly scattered replicate profiles. This is an example of a low 
		abundance transcript that produced replicate profiles scattered over a 
		two cycle region:</p>
		<p align="center">
		<b>Production of highly scattered profiles at low target concentrations</b><br>
		<img border="0" src="images/fus_undiluted.gif" width="394" height="516"></p>
		<p>LRE generated quantities (No) ranging from 1-6 molecules, with an 
		average of 4.0 molecules per <font face="Times New Roman">µ</font>l. 
		Although this suggests that quantitative 
		accuracy has been compromised, Poisson distribution provides an 
		alternative explanation:</p>
		<p align="center">&nbsp;<img border="0" src="images/poisson_distribution_graph.gif" width="532" height="372"></p>
		<p>Poisson distribution dictates that at very low target quantities the frequency of 
		aliquots (Y-axis) that will contain a specific number of target 
		molecules (X-axis) can vary considerably, and that this variance is 
		dependent on the target concentration (Z-axis). Poisson distribution 
		further predicts that for target concentrations below 0.5 molecules 
		per aliquot, the vast majority of aliquots will contain either one or 
		zero target molecules.</p>
		<p>The highly scattered replicate profiles shown above are thus 
		consistent with that predicted by Poisson distribution. Furthermore, diluting the 
		sample 10X to a predicted 0.4 N/<font face="Times New Roman">µ</font>l, 
		also produced replicate reactions that are consistent with that 
		predicted by Poisson distribution. That is, aliquots contain either no 
		target molecules (0 N) or a single target molecule (1 N): </p>
		<p align="center">
		<b>Profile clustering is restored for single molecule amplifications<br>
		</b>
		<img border="0" src="images/fus_10Xdiluted.gif" width="390" height="445"></p>
		<p align="left">
		Note that although this is a very limited dataset, 1 N profiles can also 
		be used for confirming the accuracy of optical calibration, which in 
		this example suggests that the OCF may be about 10% too high, as the 
		average over these four profiles is 0.9 molecules, 10% lower than the 
		expected 1.0 molecule. That is, the OCF to target quantity relationship 
		is linear, such that this potential 10%&nbsp; error in OCF would 
		generate a 10% error in target quantity; also note that this error 
		impacts all targets equally. </p>
		<p><b>Nil reactions are diagnostic of a key landmark for absolute 
		quantification: zero<br>
		</b>An important principle arising from absolute quantification 
		that is somewhat counter intuitive for conventional real-time qPCR 
		methods, is 
		that nil reactions are generated by zero molecule aliquots, rather than due, for example, by 
		a catastrophic enzymatic failure, or some other limitation of real-time 
		qPCR. In fact, the tight clustering of 1 N profiles is indicative of the extraordinary precision that can be achieved 
		with real-time qPCR. </p>
		<p>Quantitative accuracy can be further assessed by &quot;counting 
		molecules&quot;; that is, these profiles predict a total of four target 
		molecules within eight aliquots, predicting an average concentration of 
		0.5 N per aliquot. This agrees closely to the LRE predicted 
		quantity of 4.0 N per aliquot within the undiluted sample. This also 
		illustrates another important principle of absolute quantification, 
		which is that nil reactions (0 N) must be included into target quantity 
		determination. </p>
		<p>While a detailed overview is beyond the scope of this 
		discussion, working with single molecule profiles also provides 
		additional tools for assessing assay performance and quantitative 
		accuracy, in part because it allows quantitative 
		scale to be defined without the need to apply an external quantitative standard. An example is presented in the <a href="lda_overview.html">LDA 
		Overview</a> that describes the ability to conduct absolute 
		quantification independent of the optical and kinetic parameters of 
		real-time qPCR, which is also the foundation upon which digital 
		PCR is based.</p>
		<p><b>The&nbsp; &lt;10 molecule problem<br>
		</b>These examples illustrate two key phenomenon that impact 
		LRE quantification when working with target quantities below 10 
		molecules. The first is that extensive scattering of amplification profiles 
		precludes the ability to generate an
		<a href="../glossary/glossary.html#Average_Profile">average profile</a>. 
		The second is the necessity of averaging target quantities generated by 
		individual replicate profiles, including nil reactions, in order to accurately determine target quantity.&nbsp; </p>
		<p>Thus, when a target quantity of &lt;10 molecules is encountered, the LRE 
		Analyzer will report target quantity as an average of the replicate profiles, 
		as indicated within the average profile label: </p>
		<p align="center">
		&nbsp;<img border="0" src="images/below_10_molecules_labeling.gif" width="294" height="55"></p>
		<p>See also:<br>
		<a href="assessing_accuracy.html">Assessing of Quantitative Accuracy</a></p>
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